We investigate lower bounds to the time-smeared energy density, so-called quantum energy inequalities (QEI), in the class of integrable models of quantum field theory. Our main results are a state-independent QEI for models with constant scattering function and a QEI at one-particle level for generic models. In the latter case, we classify the possible form of the stress-energy tensor from first principles and establish a link between the existence of QEIs and the large-rapidity asymptotics of the two-particle form factor of the energy density. Concrete examples include the Bullough–Dodd, the Federbush, and the O(n)-nonlinear sigma models.

我们研究量子场论可积模型类中时间涂抹能量密度的下界，即所谓的量子能量不等式（QEI）。我们的主要结果是具有恒定散射函数的模型的状态无关 QEI 和通用模型的单粒子级别的 QEI。在后一种情况下，我们根据第一原理对应力-能量张量的可能形式进行分类，并在 QEI 的存在与能量密度的双粒子形状因子的大快速渐近之间建立联系。具体示例包括 Bullough-Dodd、Federbush 和O ( n )-非线性 sigma 模型。